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Each of the two equations describes a flow in one compartment of a porous
medium. The equations are based on the Darcy flow and the i-th compartment is
defined in .

where is the local permeability of the i-th compartment,
is the perfusion coefficient
related to the compartments and , are
sources or sinks which represent the external flow into the i-th
compartment and is the pressure in the i-th compartment.